Question

The function f(x) = 2,5000(1+0.021/365)³⁶⁵ᵗ models the balance in a savings account. Which statement accurately describes the account?

A.The account had an initial balance of $2,500 and compounds monthly at an annual interest rate of 2.1%.
B.The account had an initial balance of $2,500 and compounds yearly at an annual interest rate of 2.1%.
C.The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 0.21%.
D.The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 2.1%.

Answer 1

The function f(x) represents a savings account with an initial balance of $2,500 that compounds interest daily at an annual rate of 2.1%. Hence the correct answer is option D

Step-by-step explanation:

The function f(x) = 2,5000(1+0.021/365)³⁶⁵ᵗ models the balance in a savings account. To determine which statement accurately describes the account, let's analyze the components of the function. The initial balance is the coefficient at the beginning of the equation which is $2,500. The interest rate is represented by the number inside the parentheses; in this case, it's 0.021, which is 2.1% expressed as a decimal. The fraction ⅔⅓⅕ indicates that the interest is being compounded daily, as there are 365 days in a year. The exponent at the end, 365t, where t is the number of years, further confirms that compounding occurs daily for each day of the year. Therefore, the correct statement is:

D. The account had an initial balance of $2,500 and compounds daily at an annual interest rate of 2.1%.